1. Technical Field
Example embodiments relate to methods for performing ion trap mass spectroscopy.
2. Description of Related Art
Penning trap mass spectrometry is a widely-used mass spectrometry method in terms of resolution and precision. Consequently, the precision of the method renders it suitable for some of the more demanding experiments being conducted in fundamental physics. In addition, the high resolving power of Penning trap mass spectrometry makes it a valuable tool in many chemical and biological applications.
Ion motion within a Penning trap is discussed in a number of references readily available to those ordinarily skilled in the art. In general, charged particles are confined in a Penning trap as the result of a combination of a homogeneous magnetic field and a static quadrupole electric field. In discussing Penning traps, the coordinate system is typically chosen so that the magnetic field is directed along the z-axis:{right arrow over (B)}=B0{right arrow over (k)}={0,0,B0},  (1)wherein B0 is the strength of the magnetic field. The magnetic field tends to confine the particles in the direction perpendicular to the direction of the magnetic field, thereby forcing the particles into generally circular orbits around the magnetic field lines. The circular orbits may be referred to as the cyclotron motion of the particles. To confine the charged particles in the direction along the magnetic field, a quadrupole electrostatic field is provided in conjunction with the magnetic field:
                                          E            →                    =                                    ∇              →                        ⁢                          V              ⁡                              (                                  x                  ,                  y                  ,                  z                                )                                                    ,                            (        2        )                                                                                    V                ⁡                                  (                                      x                    ,                    y                    ,                    z                                    )                                            =                            ⁢                                                                    V                    0                                                        2                    ⁢                                          d                      2                                                                      ⁢                                  (                                                            z                      2                                        -                                                                                            x                          2                                                +                                                  y                          2                                                                    2                                                        )                                                                                                                        =                                ⁢                                                                            V                      0                                                              2                      ⁢                                              d                        2                                                                              ⁢                                      (                                                                  z                        2                                            -                                                                        r                          2                                                2                                                              )                                                              ,                                                          (        3        )            where d is the characteristic trap size and V0 is the magnitude of the trapping potential. The electric field creates a harmonic potential well along the z-axis, and the motion of the trapped particle is that of a harmonic oscillator:z(t)=Az cos(ωzt+φz),  (4)where Az is the amplitude of the axial oscillatory motion, ωz =√{square root over (qV0/mr02)} is the angular frequency of the axial oscillatory motion, and φz is the phase of the axial oscillatory motion.
FIG. 1 is an illustration of a conventional Penning trap mass spectroscopy device. Referring to FIG. 1, a conventional Penning trap mass spectroscopy device includes a magnet 1 that creates a uniform (homogeneous) magnetic field. An ion cyclotron resonance (ICR) cell 3 is placed inside a vacuum chamber that is connected to and evacuated using a suitable vacuum system 2. Generally, the ICR cell 3 is positioned so that it will be exposed to the strong homogeneous magnetic field produced by the magnet 1. Such a position is typically near the center of the volume surrounded by the magnet 1.
The ion motion in the direction perpendicular to the magnetic field direction (radial motion) is a combination of two circular motions: the fast modified cyclotron motion and the slow magnetron motion. The ion motion is described by the following expression:x(t)+iy(t)=Ã+eiω+t+Ã−eiω−t,  (5)where Ã+=A+eiφ+ is a complex constant that incorporates the amplitude and phase of the modified cyclotron motion and Ã−=A−eiφ− is a complex constant that incorporates the amplitude and phase of the magnetron motion. The angular frequencies of the magnetron motion and the modified cyclotron motion are respectively given by the following expressions:
                                                                        ω                -                            =                            ⁢                                                1                  2                                ⁢                                  (                                                            ω                      c                                        -                                                                                            ω                          c                          2                                                -                                                  2                          ⁢                                                      ω                            z                            2                                                                                                                                )                                                                                                                        =                                ⁢                                                      ω                    z                    2                                                        2                    ⁢                                          ω                      +                                                                                  ,                                                          (        6        )                                                                                    ω                +                            =                            ⁢                                                1                  2                                ⁢                                  (                                                            ω                      c                                        +                                                                                            ω                          c                          2                                                -                                                  2                          ⁢                                                      ω                            z                            2                                                                                                                                )                                                                                                                        =                                ⁢                                                      ω                    c                                    -                                      ω                    -                                                              ,                                                          (        7        )            where ωc=qB0/m is the angular frequency of the cyclotron motion of a particle in the magnetic field in the absence of a quadrupole electric field. The stability conditions for the trapped charged particle in the Penning trap dictate thatω−<ωz<ω+.  (8)
Fourier transform ion cyclotron resonance (FT-ICR) is the most widely-used method of Penning trap-based mass spectroscopy. A conventional FT-ICR method involves exciting the modified cyclotron motion of an ion “packet” placed into a Penning trap and then detecting the modified cyclotron motion by measuring the current it induces on the segmented electrodes of the Penning trap. The frequency components of the detected signal correspond to ions with different mass-to-charge ratios in the ion “packet.” This information is typically extracted from the detected signal by performing a fast Fourier transform (FFT) analysis on the digitized signal.
FIG. 2 is an illustration of a conventional FT-ICR method. FIG. 2a shows a simplified circuit for the excitation of the ion packet. FIG. 2b shows a simplified circuit for the detection of the ion packet. FIG. 2c shows a mock-up example of a stored waveform inverse Fourier transform (SWIFT) excitation waveform and its spectrum. FIG. 2d shows an example of a detected ICR signal and its spectrum for a mixture of 3 different ion species with cyclotron frequency values f=150, 500, and 510. Referring to FIGS. 2c-d, typically Trf<<Tacq.
The resolving power of the conventional FT-ICR method is determined by the acquisition time of the induced current ICR signal, which takes up the majority of the measurement cycle Tmeas≈Tacq:RFTICR≈νcTmeas;  (9)where νc=ωc/2π is the cyclotron frequency and Tmeas is the duration of the measurement cycle. The sensitivity of the conventional FT-ICR method is typically about 100 ions.
Time of flight ion cyclotron resonance (TOF-ICR) mass spectrometry is used in precision mass spectrometry and is typically performed on a single ion. Conventional TOF-ICR mass spectrometry can achieve precision on the order of δm/m<1 ppb. To determine the ion mass, the ion's magnetron motion is induced by dipole excitation at the magnetron frequency or by injecting the ion into the trap off-axis. The magnetron motion is then converted to the cyclotron motion by applying a quadrupole radio frequency (RF) field at a frequency close to the sum frequency ωrf≈ω++ω−=ωc:
                              E          →                =                              (                                          x                ⁢                                                                  ⁢                                  y                  ^                                            -                              y                ⁢                                                                  ⁢                                  x                  ^                                                      )                    ⁢                                    V              rf                                      2              ⁢                              a                2                                              ⁢                      cos            ⁡                          (                                                                    ω                    rf                                    ⁢                  t                                +                                  ϕ                  rf                                            )                                                          (        10        )            
The conversion is the most efficient when the frequency of the quadrupole signal coincides with the ion's cyclotron frequency. The conversion efficiency is determined by expelling the ion from the trap and then measuring its time of flight to a detector placed outside the strong magnetic field. As the ion exits the magnetic field, it passes the region of strong magnetic field gradient, which accelerates the ion to a degree proportional to its magnetic moment:{right arrow over (F)}=−{right arrow over (∇)}{right arrow over (μ)}{right arrow over (B)},  (11)where μ∝A+. The time of flight measurement is performed for a set of frequencies in the neighborhood of the ion cyclotron frequency ωc.
FIG. 3 is an illustration of the results of a conventional time of flight measurement. FIG. 3a shows the radial energy and the time of flight for a typical mass measurement as a function of the detuning of the quadrupole RF signal from the ion's cyclotron frequency ωc. Three characteristic points of the spectrum are identified on the graph: A, B, and C. At point A, the quadrupole RF signal is on resonance, and the time of flight is the shortest. At point B, the quadrupole RF signal is off resonance. At point C, the quadrupole RF signal is at the “satellite” resonance that appears due to the sin x/x spectrum of the square envelope of the RF signal. FIG. 3b shows ion trajectories at the beginning of the quadrupole RF excitation, in the middle, and at the end for each of points A, B, and C.
The resolving power of a conventional time of flight measurement is determined by the spectral line-width of the RF quadrupole excitation, i.e., its duration Trf. Because the majority of the measurement cycle is used for the RF excitation Tmeas≈Trf.RTOF≈νcTmeas;  (12)where Trf is the time interval during which the quadrupole excitation signal was applied, which is essentially the measurement time. With careful reduction of systematic effects, curve-fitting the resulting time-of-flight data can determine the mass with a precision of δm/m≈1/R 1/√N. The statistical factor 1/√N comes from repeating the TOF measurement N times.
Because the TOF-ICR method is not used for determining the composition of the ion mixture in the trap, but rather for determining the mass of a single ion with high precision, it is more appropriate to define the efficiency of the method rather than its sensitivity. Typically, a microchannel plate (MCP) stack is used for this purpose, with the most common detection efficiency being ≈50%.
An axial phase detection method utilizes features from both the FT-ICR and TOF-ICR methods. In a conventional axial phase detection method, an ion is initially excited into cyclotron motion and allowed to orbit around the trap center for a given period of time. At the end of that period of time, the cyclotron motion is converted to axial oscillation by applying a quadrupole RF field. This conversion is substantially identical to the magnetron-cyclotron conversion used in the TOF-ICR method. However, instead of coupling the magnetron and cyclotron motions, the cyclotron motion is coupled to the axial motion by means of quadrupole RF signal
                              E          →                =                              (                                          x                ⁢                                                                  ⁢                                  z                  ^                                            -                              z                ⁢                                                                  ⁢                                  x                  ^                                                      )                    ⁢                                    V              rf                                      2              ⁢                              a                2                                              ⁢                      cos            ⁡                          (                                                                    ω                    rf                                    ⁢                  t                                +                                  ϕ                  rf                                            )                                                          (        13        )            at the frequency ωrf tuned to the resonant coupling frequency ω+−ωz.
The axial motion of the ion is then detected by measuring the current induced by ion motion in the trap electrodes, in a manner similar to that utilized in FT-ICR detection methods. Both frequency and the phase of the axial motion are determined from the detected signal. Because the current induced by a single ion is very small, a very sensitive superconducting quantum interference device (SQUID)-based superconducting resonant circuitry is used to detect the axial motion. The additional phase information allows to achieve higher resolving power than νcTmeas, typical for any method that is not sensitive to the phase of the ion motion. The resolving power is instead
                              R          ≈                                    (                                                2                  ⁢                  π                                Δϕ                            )                        ×                          v              c                        ⁢                          T              meas                                      ,                            (        14        )            where Δφ is the uncertainty of the phase measurement. The benefit of the enhancement factor 2π/Δφ is reduced if the acquisition time of the axial motion detector is not insignificant when compared to the total time of the measurement. The detection of the accumulated phase using the SQUID detection of the axial motion typically allows determining the phase with precision Δφ=15° which corresponds to the enhancement factor of 24. The detection time of the axial motion is 4-8 seconds.
Like the TOF-ICR method, axial phase detection measurements are performed on a single ion or a pair of different ions for ultra-precise determination of their mass ratio. Thus, neither the axial phase detection ICR method nor the TOF-ICR method is particularly suitable for analyzing ion mixture compositions. Accordingly, despite the enhanced sensitivity offered by the TOF-ICR method and the resolution enhancement offered by the axial phase detection method, these methods do not rise to the same level as FT-ICR methods in the area of determining ion mixture composition.